Asian options have a payoff that is the difference between the strike price and the average value of the underlying asset over the lifetime of the contract. FinancialDerivative can price the following types of Asian options:

Barrier options have a payoff that depends on whether or not the price reaches a predetermined barrier level. The following types of barrier options are supported:

"BarrierDownIn"

barrier down-and-in option

"BarrierDownOut"

barrier down-and-out option

"BarrierUpIn"

barrier up-and-in option

"BarrierUpOut"

barrier up-and-out option

Barrier up-and-out options become void if the price rises to or exceeds the barrier level. Down-and-out options become void if the price decreases to the barrier. Up-and-in options become valid as the price rises to the barrier level. Down-and-in options become valid when the price falls to or below the barrier level.

All single-barrier options require the following parameters:

"Barrier"

barrier level

"Expiration"

expiration date, or time to maturity

"Rebate"

rebate paid to option holder if the option expires void

"StrikePrice"

strike price

FinancialDerivative supports call and put barrier options with European and American exercise styles. All rebates are paid at option expiration.

Binary Options

Binary or digital options have a payoff at maturity that is either a fixed amount or nothing.

"BinaryCash"

binary cash-or-nothing option

"BinaryAsset"

binary asset-or-nothing option

Binary cash-or-nothing options pay a fixed amount if the underlying price is in the money at maturity. Binary asset-or-nothing options pay the current price of the asset at expiration if the price of the asset is above the strike price.

Binary options require the following parameters:

"Expiration"

expiration date, or time to maturity

"StrikePrice"

strike price

FinancialDerivative supports binary call and put options with European exercise style. The payoff is taken to be 1 for the binary cash option.

Chooser Options

A chooser option is a compound contract that requires the buyer to choose between a call and a put option on the same underlying asset at a predetermined expiration time.

Double-barrier options have a payoff that depends on whether or not the price of the underlying asset reaches either of the two barrier levels at any time prior to exercise. The following types of double-barrier options are supported:

"DoubleBarrierKnockOut"

double barrier knock-out option

"DoubleBarrierKnockIn"

double barrier knock-in option

A double-barrier knock-out option becomes void as soon as the price of the underlying asset breaks out of the barrier interval. A double-barrier knock-in option becomes valid as soon as the price breaks out of the interval.

Required contract parameters:

"Expiration"

expiration date, or time to maturity

"StrikePrice"

contract strike price

"Barriers"

barrier interval in the form

FinancialDerivative supports double-barrier call and put options with either American or European exercise style.

Extendible Options

Extendible options can be exercised at the time of maturity, or they can be extended by a predetermined period. The following types of extendible options are supported:

"ExtendibleHolder"

holder-extendible option

"ExtendibleWriter"

writer-extendible option

A holder-extendible option requires the holder to pay an additional premium to extend the option. A writer-extendible option is extended automatically if the option is out of the money upon initial expiration.

A lookback contract is a path-dependent option whose value at exercise depends on the optimal price of the underlying asset over the lifetime of the contract. The following lookback options are supported:

"LookbackFloating"

floating-strike lookback option

"LookbackFixed"

fixed-strike lookback option

In a floating-strike lookback call option, the strike price is taken to be the lowest price attained by the underlying asset over the option's lifetime. For put options, the highest underlying price is used.

In a fixed-strike lookback call option, the value of the underlying asset at exercise is taken to be the highest price of the underlying asset over the option's lifetime. For put options, the lowest underlying price is used.

Required contract parameters:

"Expiration"

expiration date, or time to maturity

"StrikePrice"

contract strike price ( only)

"MaxSoFar"

highest value attained by the asset over the contract period to date ( call option or put option)

"MinSoFar"

lowest value attained by the asset over the contract period to date ( put option or call option)

FinancialDerivative supports lookback call and put options with European exercise style. In addition, it supports American exercise for floating-strike lookback options.

One-Touch Options

A one-touch contract is a binary option with an American exercise style.

"OneTouch"

one touch option

One-touch options pay a fixed amount at an arbitrary exercise time if the option is in the money.

A perpetual lookback contract is a lookback contract without an expiration date.

"PerpetualLookback"

floating-strike perpetual lookback option

In a floating-strike perpetual lookback call option, the strike price adjusts to the lowest price attained by the asset over the contract period so far. For put options, the strike price is taken to be the highest underlying price so far.

A power option is a contract for which the payoff is raised to a power.

"Power"

power option

"Powered"

powered option

"PowerCapped"

capped power option

A power option raises the price of the underlying asset at time of exercise to the power specified. A powered option raises the difference between the price of the underlying asset and the strike price to the power specified. A capped power option caps the payoff on a power option.

Required contract parameters:

"Expiration"

expiration date, or time to maturity

"StrikePrice"

contract strike price

"Power"

the power

"Cap"

the maximum payoff (capped power option)

Russian Options

A Russian option is a type of perpetual lookback call option for which the payoff is the highest value attained by the underlying asset by exercise time.

"Russian"

fixed-strike perpetual lookback option

Required contract parameters:

"MaxSoFar"

highest asset value over the contract period to date

Vanilla Options

A vanilla option contract is a path-independent option.

"Vanilla"

vanilla option

Required contract parameters:

"Expiration"

expiration date, or time to maturity

"StrikePrice"

contract strike price

FinancialDerivative supports vanilla call and put options with either an American or a European exercise style. The name specification can be omitted.

By default, FinancialDerivative prices American vanilla options by numerically solving the Black–Scholes partial differential equation. A binomial tree solution method can be specified by setting the Method option to .

Rainbow Options

A rainbow contract entitles the option holder to the maximum of the payouts generated by the individual components of a basket of assets.

Option names:

"RainbowBest"

payout is the value of the best-performing asset

"RainbowWorst"

payout is the value of the worst-performing asset

"RainbowMoney"

payout is based on the value of the best-performing asset, where a risk-free investment is one of the assets

Required contract parameters:

"Expiration"

expiration date, or time to maturity

"Money"

amount of cash in the basket ( option)

FinancialDerivative supports rainbow options with American and European exercise styles. American exercise is supported for a maximum of two non-cash assets in a basket.

Rainbow Minimum and Maximum Options

A rainbow minimum contract has a payout that is the value of an option on the worst-performing asset for a call, and on the best-performing asset for a put. A rainbow maximum contract has a payout that is the value of an option on the best-performing asset for a call, and on the worst-performing asset for a put.

Option names:

"RainbowMin"

rainbow minimum contract

"RainbowMax"

rainbow maximum contract

Required contract parameters:

"Expiration"

expiration date, or time to maturity

"StrikePrice"

contract strike price

FinancialDerivative supports rainbow minimum and maximum call and put options with American and European exercise styles. American exercise is supported for a maximum of two assets in a basket.

Mountain Range Options

Mountain range options are a class of contracts that entitle the holder to a payout that is based on the performance of a basket of assets, with certain time constraints on asset performance.

"Altiplano"

Altiplano mountain range contract

"Annapurna"

Annapurna mountain range contract

"Atlas"

Atlas mountain range contract

"Everest"

Everest mountain range contract

"Himalaya"

Himalaya mountain range contract

Exercise and option type specifications are not applicable to mountain range options.

An Altiplano contract is a type of mountain range option that pays out a fixed coupon amount if none of the basket assets have reached their respective barriers, and nothing otherwise.

Parameters for Altiplano contracts:

"Barriers"

barrier values of each asset

"Coupon"

coupon amount

"Expiration"

expiration date, or time to maturity

An Annapurna contract pays out a fixed coupon amount if none of the basket assets descend below their respective fractional barrier prices, and nothing otherwise.

Parameters for Annapurna options:

"Fractions"

asset price fractions that trigger the validity condition

"Coupon"

coupon amount

"Expiration"

expiration date, or time to maturity

An Atlas contract has a payout that is based on the performance of a basket from which the best- and worst-performing assets have been removed.

Parameters for Atlas contracts:

"StrikePrice"

strike price of the option, expressed as a multiplicative factor

"NominalAmount"

cash amount on which the returns of the option accrue

"Expiration"

expiration date, or time to maturity

An Everest contract has a payout that is based on the performance of the worst asset in a basket of assets.

Parameters for Everest contracts:

"NominalAmount"

cash amount on which the returns of the option accrue

"Expiration"

expiration date, or time to maturity

A Himalaya contract has a payout that is based on the performance of the best asset in a gradually shrinking basket of assets. The time to expiration is divided into subperiods, with the yield for each subperiod determined by the return on the best-performing asset over that period, and with each asset being used to determine a subperiod return exactly once.

Parameters for Himalaya contracts:

"NominalAmount"

cash amount on which the returns of the option accrue

"Expiration"

expiration date, or time to maturity

Spread Options

A spread contract is a multi-asset option whose value depends on the difference between the values of the underlying assets at the time of exercise.

"Spread"

two-asset spread option

Required contract parameters:

"Expiration"

expiration date, or time to maturity

"StrikePrice"

contract strike price

FinancialDerivative supports spread call and put options with American and European exercise styles.

Quanto Vanilla Options

A Quanto vanilla contract is an option whose value at exercise depends on the performance of the underlying asset, as well as on the performance of the currency in which the asset is denominated.

Option names:

"QuantoFixedExchange"

vanilla fixed-exchange Quanto option

"QuantoFixedStrike"

vanilla fixed-strike Quanto option

A vanilla fixed-exchange Quanto option is settled at a predetermined exchange rate. A vanilla fixed-strike Quanto option is settled at a fixed strike price in a foreign currency at the prevailing exchange rate.

Required contract parameters:

"Expiration"

expiration date, or time to maturity

"StrikePrice"

contract strike price

FinancialDerivative supports vanilla Quanto call and put options with American and European exercise styles.